Problem: Simplify the following expression: $ a = \dfrac{4}{9} - \dfrac{9r - 2}{-4} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-4}{-4}$ $ \dfrac{4}{9} \times \dfrac{-4}{-4} = \dfrac{-16}{-36} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{9r - 2}{-4} \times \dfrac{9}{9} = \dfrac{81r - 18}{-36} $ Therefore $ a = \dfrac{-16}{-36} - \dfrac{81r - 18}{-36} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{-16 - (81r - 18) }{-36} $ Distribute the negative sign: $a = \dfrac{-16 - 81r + 18}{-36}$ $a = \dfrac{-81r + 2}{-36}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{81r - 2}{36}$